On the connections between the topological genus of certain polyhedra and the algebraic genus of their Hilton-Hopf quadratic forms
- Autores: Imre Bokor
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 34, Nº 2, 1990, págs. 323-333
- Idioma: inglés
- DOI: 10.5565/publmat_34290_12
- Títulos paralelos:
- Sobre la conexión entre el género topológico de ciertos poliedros y el género algebraico de sus formas cuadráticas de Hilton-Hopt
- Enlaces
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Resumen
The Hilton-Hopf quadratic form is defined for spaces of the homotopy type of a CW complex with one cell each in dimensions 0 and 4n, K cells in dimension 2n and no other cells. If two such spaces are of the same topological genus, then their Hilton-Hopf quadratic forms are of the same weak algebraic genus. For large classes of spaces, such as simply connected differentiable 4-manifolds, the converse is also true, as long as the suspensions of the spaces are also of the same topological genus. This note allays the conjecture that the converse is true in general by offering two techniques for generating infinite families of counterexamples.
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